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Semiparametric tests for seasonal unit roots based on a semiparametric feasible GLSE

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  • Shin, Dong Wan
  • Oh, Man-Suk

Abstract

Semiparametric extensions of the seasonal unit root tests for the model of Dickey et al. (1984, J. Amer. Statist. Assoc. 79, 355) are proposed. Development of semiparametric extensions based on the ordinary least-squares estimator (OLSE) is impossible for the regression of Dickey et al. (1984) since the limiting null distribution of the OLSE-based test statistic is entangled with nuisance parameters under the usual normalization. This is in contrast with the successful development of the OLSE-based semiparametric unit root tests of Phillips (Econometrica 55 (1987) 277). To overcome the difficulty, we propose tests based on a feasible generalized least-squares estimator (GLSE), instead of the OLSE, and the spectral decomposition of the generalized sum of products of the regressor variables. The key advantage of the proposed method is that one can construct the feasible GLSE and hence tests of the seasonal unit root without specifying a parametric model for the error process.

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  • Shin, Dong Wan & Oh, Man-Suk, 2000. "Semiparametric tests for seasonal unit roots based on a semiparametric feasible GLSE," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 207-218, November.
    • Handle: RePEc:eee:stapro:v:50:y:2000:i:3:p:207-218
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    1. Joseph Beaulieu, J. & Miron, Jeffrey A., 1993. "Seasonal unit roots in aggregate U.S. data," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 305-328.
    2. Amsler, Christine & Lee, Junsoo, 1995. "An LM Test for a Unit Root in the Presence of a Structural Change," Econometric Theory, Cambridge University Press, vol. 11(2), pages 359-368, February.
    3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    4. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
    5. Breitung, Jörg & Franses, Philip Hans, 1998. "On Phillips–Perron-Type Tests For Seasonal Unit Roots," Econometric Theory, Cambridge University Press, vol. 14(2), pages 200-221, April.
    6. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    7. Ghysels, Eric & Lee, Hahn S. & Noh, Jaesum, 1994. "Testing for unit roots in seasonal time series : Some theoretical extensions and a Monte Carlo investigation," Journal of Econometrics, Elsevier, vol. 62(2), pages 415-442, June.
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    Cited by:

    1. Shin, Dong Wan & Oh, Man-Suk, 2004. "Fully modified semiparametric GLS estimation for regressions with nonstationary seasonal regressors," Journal of Econometrics, Elsevier, vol. 122(2), pages 247-280, October.
    2. Shin, Dong Wan, 2004. "Estimation of spectral density for seasonal time series models," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 149-159, April.

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